- Title Pages
- Dedication
- Introduction
- Definitions
- Note on the Illustrations
- Part 1 Numerals: Significant Manuscripts and Initiators
- Chapter 1 Curious Beginnings
- Chapter 2 Certain Ancient Number Systems
- Chapter 3 Silk and Royal Roads
- Chapter 4 The Indian Gift
- Chapter 5 Arrival in Europe
- Chapter 6 The Arab Gift
- Chapter 7 <i>Liber Abbaci</i>
- Chapter 8 Refuting Origins
- Part 2 Algebra
- Chapter 9 Sans Symbols
- Chapter 10 Diophantus’s <i>Arithmetica</i>
- Chapter 11 The Great Art
- Chapter 12 Symbol Infancy
- Chapter 13 The Timid Symbol
- Chapter 14 Hierarchies of Dignity
- Chapter 15 Vowels and Consonants
- Chapter 16 The Explosion
- Chapter 17 A Catalogue of Symbols
- Chapter 18 The Symbol Master
- Chapter 19 The Last of the Magicians
- Part 3 The Power of Symbols
- Chapter 20 Rendezvous in the Mind
- Chapter 21 The Good Symbol
- Chapter 22 Invisible Gorillas
- Chapter 23 Mental Pictures
- Chapter 24 Conclusion
- Appendix A Leibniz’s Notation
- Appendix B Newton’s Fluxion of <i>x<sup>n</sup></i>
- Appendix C Experiment
- Appendix D Visualizing Complex Numbers
- Appendix E Quaternions
- Acknowledgments
- Index

# Refuting Origins

# Refuting Origins

- Chapter:
- (p.73) Chapter 8 Refuting Origins
- Source:
- Enlightening Symbols
- Author(s):
### Joseph Mazur

- Publisher:
- Princeton University Press

This chapter discusses the debate among experts over the origins of the Hindu-Arabic numerals. One such expert was the French mathematician and historian Michel Chasles, who argued that by the fifth century, France already had a decimal place-value system for computations documented in Boethius's *Arithmetic*, which seemed to use a multiplication table with Arabic numbers. For much of the nineteenth century, the Indian origin of positional decimal notation had been challenged. The chapter also considers the claim made by George Rusby Kaye in 1907 that the numerals and the decimal system could not have been Indian in origin and that the history of Hindu-Arabic number representation was complicated by the existence of so many forgeries of the time. Whatever the truth, it is quite likely that sometime in the fifth century, Indian numbers had come to Alexandria via a trade route through Syria before moving westward.

*Keywords:*
place-value, Hindu-Arabic numerals, Michel Chasles, France, decimal system, Arabic numbers, George Rusby Kaye, forgeries, Indian numbers, Alexandria

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- Title Pages
- Dedication
- Introduction
- Definitions
- Note on the Illustrations
- Part 1 Numerals: Significant Manuscripts and Initiators
- Chapter 1 Curious Beginnings
- Chapter 2 Certain Ancient Number Systems
- Chapter 3 Silk and Royal Roads
- Chapter 4 The Indian Gift
- Chapter 5 Arrival in Europe
- Chapter 6 The Arab Gift
- Chapter 7 <i>Liber Abbaci</i>
- Chapter 8 Refuting Origins
- Part 2 Algebra
- Chapter 9 Sans Symbols
- Chapter 10 Diophantus’s <i>Arithmetica</i>
- Chapter 11 The Great Art
- Chapter 12 Symbol Infancy
- Chapter 13 The Timid Symbol
- Chapter 14 Hierarchies of Dignity
- Chapter 15 Vowels and Consonants
- Chapter 16 The Explosion
- Chapter 17 A Catalogue of Symbols
- Chapter 18 The Symbol Master
- Chapter 19 The Last of the Magicians
- Part 3 The Power of Symbols
- Chapter 20 Rendezvous in the Mind
- Chapter 21 The Good Symbol
- Chapter 22 Invisible Gorillas
- Chapter 23 Mental Pictures
- Chapter 24 Conclusion
- Appendix A Leibniz’s Notation
- Appendix B Newton’s Fluxion of <i>x<sup>n</sup></i>
- Appendix C Experiment
- Appendix D Visualizing Complex Numbers
- Appendix E Quaternions
- Acknowledgments
- Index